SOLUTION: Solve the following equation in the interval [0, 2pi]. Give the answer as a multiple of pi. Do not use decimal numbers. The answer should be a fraction or an integer. 2(cos(t))^

Algebra ->  Trigonometry-basics -> SOLUTION: Solve the following equation in the interval [0, 2pi]. Give the answer as a multiple of pi. Do not use decimal numbers. The answer should be a fraction or an integer. 2(cos(t))^      Log On


   

Question 928167: Solve the following equation in the interval [0, 2pi].
Give the answer as a multiple of pi. Do not use decimal numbers. The answer should be a fraction or an integer.
2(cos(t))^2-cos(t)-1=0
Help would be appreciated.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Substitute,
u=cos%28t%29
Then,
2u%5E2-u-1=0
%28u-1%29%282u%2B1%29=0
Two "u" solutions:
u-1=0
u=1
cos%28t%29=1
t=0
and
2u%2B1=0
2u=-1
u=-1%2F2
cos%28t%29=-1%2F2
t=%282%2F3%29pi and t=%284%2F3%29pi